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library(readxl)
library(ggpubr)
## Loading required package: ggplot2
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(effectsize)
library(effsize)
Dataset6.1 <- read_excel("C:/Users/tanie/Downloads/Dataset6.1.xlsx")
Dataset6.1 %>%
  group_by(Group) %>%
  summarise(
    Mean = mean(Exam_Score, na.rm = TRUE),
    Median = median(Exam_Score, na.rm = TRUE),
    SD = sd(Exam_Score, na.rm = TRUE),
    N = n()
  )
## # A tibble: 2 × 5
##   Group        Mean Median    SD     N
##   <chr>       <dbl>  <dbl> <dbl> <int>
## 1 No Tutoring  71.9   71.5  7.68    40
## 2 Tutoring     78.4   78.7  7.18    40
hist(Dataset6.1$Exam_Score[Dataset6.1$Group == "Tutoring"],
     main = "Histogram of Tutoring Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

hist(Dataset6.1$Exam_Score[Dataset6.1$Group == "No Tutoring"],
     main = "Histogram of No Tutoring Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

For the tutoring histogram, the data appears symetrically skewed. The kurtosis appears bell-shaped (normal).

For the no tutoring histogram, the data appears symmetrical (normal). The kurtosis also appears bell-shaped (normal).

ggboxplot(Dataset6.1, x = "Group", y = "Exam_Score",
          color = "Group",
          palette = "jco",
          add = "jitter")

The tutoring boxplot appears normal. There are dots past the whiskers.

The no tutoring boxplot appears abnormal. There are several dots past the whiskers. Although some are very close to the whiskers, some are arguably far away.

shapiro.test(Dataset6.1$Exam_Score[Dataset6.1$Group == "No Tutoring"])
## 
##  Shapiro-Wilk normality test
## 
## data:  Dataset6.1$Exam_Score[Dataset6.1$Group == "No Tutoring"]
## W = 0.98791, p-value = 0.9398
shapiro.test(Dataset6.1$Exam_Score[Dataset6.1$Group == "Tutoring"])
## 
##  Shapiro-Wilk normality test
## 
## data:  Dataset6.1$Exam_Score[Dataset6.1$Group == "Tutoring"]
## W = 0.98859, p-value = 0.953

The data for tutoring was normal (p > .05). The data for no tutoring was normal (p > .05).

t.test(Exam_Score ~ Group, data = Dataset6.1, var.equal = TRUE)
## 
##  Two Sample t-test
## 
## data:  Exam_Score by Group
## t = -3.8593, df = 78, p-value = 0.000233
## alternative hypothesis: true difference in means between group No Tutoring and group Tutoring is not equal to 0
## 95 percent confidence interval:
##  -9.724543 -3.105845
## sample estimates:
## mean in group No Tutoring    mean in group Tutoring 
##                  71.94627                  78.36147

p < .05, (less than .05), this means the results are SIGNIFICANT.

cohens_d(Exam_Score ~ Group, data = Dataset6.1, pooled_sd = TRUE)
## Cohen's d |         95% CI
## --------------------------
## -0.86     | [-1.32, -0.40]
## 
## - Estimated using pooled SD.

the effect size -0.86 meaning that there is a large difference between tutoring and not tutoring group. Tutoring (M = 78.40, SD = 7.18) were significantly different from Females (M = 71.9, SD = 7.68) in exam scores, t(78) = -3.85, p = .0002. The effect size was large (Cohen’s d = -0.86).